The Finite Moment Log Stable Process and Option Pricing

Authors: Carr P.¹; Wu L.²

Source: The Journal of Finance, Volume 58, Number 2, April 2003 , pp. 753-778(26)

Publisher: Blackwell Publishing

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Abstract:

We document a surprising pattern in S&P 500 option prices. When implied volatilities are graphed against a standard measure of moneyness, the implied volatility smirk does not flatten out as maturity increases up to the observable horizon of two years. This behavior contrasts sharply with the implications of many pricing models and with the asymptotic behavior implied by the central limit theorem (CLT). We develop a parsimonious model which deliberately violates the CLT assumptions and thus captures the observed behavior of the volatility smirk over the maturity horizon. Calibration exercises demonstrate its superior performance against several widely used alternatives.

Document Type: Research article

DOI: 10.1111/1540-6261.00544

Affiliations: 1: Courant Institute, New York University 2: Graduate School of Business, Fordham University

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